We describe the basic and exceptional calculation abilities of a calculating prodigy whose performances were investigated in single- and multi-digit number multiplication, numerical comparison, raising of powers, and short-term memory tasks. The study shows how the highly efficient long-term memory storage and retrieval processes of this calculating prodigy, his knowledge of calculation algorithms, and his good short-term memory capacity all contribute to his calculation expertise. Moreover, his pattern of performance in tasks based on memory retrieval strategies sheds new light on the problem-size/difficulty effect exhibited by normal subjects in basic arithmetical operations. When direct memory retrieval is the only strategy used by this calculating prodigy to answer a problem, the size of the item and the size of the answer do not affect the response latency. This result supports interpretations of the problem-size/difficulty effect in terms of learning and practice, and challenges interpretations in terms of magnitude itself.